In which of the following reactions, increase in temperature as well as decrease in pressure shift the equilibrium towards the forward direction :
(i)`PCl_5(g) hArr PCl_3(g) + Cl_2(g) " " DeltaH`=+ve
(ii)`N_2(g) + O_2(g) hArr 2NO(g) " " DeltaH`=+ve
(iii) `2SO_2(g) + O_2(g) hArr 2SO_3(g) " " DeltaH`=-ve
(iv) `N_2O_4 (g) hArr 2NO_2(g) " " DeltaH` =+ve

Answer

To determine which of the given reactions shift the equilibrium towards the forward direction with an increase in temperature and a decrease in pressure, we will apply Le Chatelier's Principle.

### Step-by-Step Solution:

1. **Understanding Le Chatelier's Principle**:
- Le Chatelier's Principle states that if an external change is applied to a system at equilibrium, the system will adjust itself to counteract that change and restore a new equilibrium.
- An increase in temperature favors endothermic reactions (which absorb heat), while a decrease in pressure favors the side of the reaction with more moles of gas.

2. **Analyzing Each Reaction**:
- **(i) `PCl5(g) ⇌ PCl3(g) + Cl2(g)` (ΔH = +ve)**:
- This reaction is endothermic (ΔH is positive).
- Increasing temperature will favor the forward reaction.
- The forward reaction has 2 moles of gas (1 PCl3 + 1 Cl2) compared to 1 mole of PCl5.
- Decreasing pressure will also favor the forward direction (more moles).
- **Conclusion**: Forward direction favored.

- **(ii) `N2(g) + O2(g) ⇌ 2NO(g)` (ΔH = +ve)**:
- This reaction is also endothermic.
- Increasing temperature will favor the forward reaction.
- The number of moles is the same on both sides (2 moles on the reactants side and 2 moles on the products side).
- Decreasing pressure has no effect on the equilibrium position.
- **Conclusion**: Forward direction favored due to temperature, but pressure has no effect.

- **(iii) `2SO2(g) + O2(g) ⇌ 2SO3(g)` (ΔH = -ve)**:
- This reaction is exothermic (ΔH is negative).
- Increasing temperature will favor the reverse reaction (not forward).
- The forward reaction has 3 moles of gas (2 SO2 + 1 O2) compared to 2 moles of SO3.
- Decreasing pressure would favor the forward direction, but since temperature does not favor it, the overall effect is not forward.
- **Conclusion**: Not favored.

- **(iv) `N2O4(g) ⇌ 2NO2(g)` (ΔH = +ve)**:
- This reaction is endothermic.
- Increasing temperature will favor the forward reaction.
- The forward reaction has 2 moles of gas (2 NO2) compared to 1 mole of N2O4.
- Decreasing pressure will favor the forward direction (more moles).
- **Conclusion**: Forward direction favored.

3. **Final Result**:
- The reactions that shift towards the forward direction with an increase in temperature and a decrease in pressure are:
- (i) `PCl5(g) ⇌ PCl3(g) + Cl2(g)`
- (iv) `N2O4(g) ⇌ 2NO2(g)`